{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:LYKFZBEQQ4C2Z2LL7LH5ZCM7DU","short_pith_number":"pith:LYKFZBEQ","schema_version":"1.0","canonical_sha256":"5e145c84908705ace96bfacfdc899f1d34b567b9a178e73fbc7b359a335647b6","source":{"kind":"arxiv","id":"1703.08766","version":1},"attestation_state":"computed","paper":{"title":"Braces and symmetric groups with special conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Agata Smoktunowicz, Ferran Ced\\'o, Tatiana Gateva-Ivanova","submitted_at":"2017-03-26T04:32:28Z","abstract_excerpt":"We study symmetric groups and left braces satisfying special conditions, or identities. We are particularly interested in the impact of conditions like $\\textbf{Raut}$ and $\\textbf{lri}$ on the properties of the symmetric group and its associated brace. We show that the symmetric group $G=G(X,r)$ associated to a nontrivial solution $(X,r)$ has multipermutation level $2$ if and only if $G$ satisfies $\\textbf{lri}$. In the special case of a two-sided brace we express each of the conditions $\\textbf{lri}$ and $\\textbf{Raut}$ as identities on the associated radical ring $G_*$. We apply these to co"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1703.08766","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-03-26T04:32:28Z","cross_cats_sorted":[],"title_canon_sha256":"360746399c3d0f351885d5fb7d360d1bea775d5108af1e15d82073dd805db9d5","abstract_canon_sha256":"e179d65ba45ae48cd843d000fa645ffcce647d2ac7b72d61dada1dbd79f0ca48"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:55.622507Z","signature_b64":"6N3UrirKtNsGXMMRqFns+4ynVBeBzuMCWB6cW8tQTSbhbwYPQvWWFcBNdcNawyy9wFT90jw/4hpasCMUQ/VmCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e145c84908705ace96bfacfdc899f1d34b567b9a178e73fbc7b359a335647b6","last_reissued_at":"2026-05-18T00:47:55.621797Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:55.621797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Braces and symmetric groups with special conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Agata Smoktunowicz, Ferran Ced\\'o, Tatiana Gateva-Ivanova","submitted_at":"2017-03-26T04:32:28Z","abstract_excerpt":"We study symmetric groups and left braces satisfying special conditions, or identities. We are particularly interested in the impact of conditions like $\\textbf{Raut}$ and $\\textbf{lri}$ on the properties of the symmetric group and its associated brace. We show that the symmetric group $G=G(X,r)$ associated to a nontrivial solution $(X,r)$ has multipermutation level $2$ if and only if $G$ satisfies $\\textbf{lri}$. In the special case of a two-sided brace we express each of the conditions $\\textbf{lri}$ and $\\textbf{Raut}$ as identities on the associated radical ring $G_*$. We apply these to co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08766","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.08766","created_at":"2026-05-18T00:47:55.621878+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.08766v1","created_at":"2026-05-18T00:47:55.621878+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08766","created_at":"2026-05-18T00:47:55.621878+00:00"},{"alias_kind":"pith_short_12","alias_value":"LYKFZBEQQ4C2","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"LYKFZBEQQ4C2Z2LL","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"LYKFZBEQ","created_at":"2026-05-18T12:31:28.150371+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LYKFZBEQQ4C2Z2LL7LH5ZCM7DU","json":"https://pith.science/pith/LYKFZBEQQ4C2Z2LL7LH5ZCM7DU.json","graph_json":"https://pith.science/api/pith-number/LYKFZBEQQ4C2Z2LL7LH5ZCM7DU/graph.json","events_json":"https://pith.science/api/pith-number/LYKFZBEQQ4C2Z2LL7LH5ZCM7DU/events.json","paper":"https://pith.science/paper/LYKFZBEQ"},"agent_actions":{"view_html":"https://pith.science/pith/LYKFZBEQQ4C2Z2LL7LH5ZCM7DU","download_json":"https://pith.science/pith/LYKFZBEQQ4C2Z2LL7LH5ZCM7DU.json","view_paper":"https://pith.science/paper/LYKFZBEQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.08766&json=true","fetch_graph":"https://pith.science/api/pith-number/LYKFZBEQQ4C2Z2LL7LH5ZCM7DU/graph.json","fetch_events":"https://pith.science/api/pith-number/LYKFZBEQQ4C2Z2LL7LH5ZCM7DU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LYKFZBEQQ4C2Z2LL7LH5ZCM7DU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LYKFZBEQQ4C2Z2LL7LH5ZCM7DU/action/storage_attestation","attest_author":"https://pith.science/pith/LYKFZBEQQ4C2Z2LL7LH5ZCM7DU/action/author_attestation","sign_citation":"https://pith.science/pith/LYKFZBEQQ4C2Z2LL7LH5ZCM7DU/action/citation_signature","submit_replication":"https://pith.science/pith/LYKFZBEQQ4C2Z2LL7LH5ZCM7DU/action/replication_record"}},"created_at":"2026-05-18T00:47:55.621878+00:00","updated_at":"2026-05-18T00:47:55.621878+00:00"}